That said, I remain stunned that UK ATC doesn't have some sort of precip picture superimposable.
Yup, me to. Fly 30 mins across the North Sea to Holland and they have a good system which seems to match what you see on the aircraft radar very well. Saves a huge amount of RT time and helps keep the traffic flowing, ATC just vector you around most severe weather without asking as they can see the bad stuff quite clearly. At some point in the UK somebody made the decision not to have it and in my opinion they got it VERY wrong.